Digital signal sampling is utilized in many different applications, such as signal (data, speech, video, etc.) processing, high-speed data converters, data communication devices, such as receivers and transmitters and the like.
A sampling rate refers to the frequency of analog to digital conversion employed to capture information contained in an analog signal. To allow a complete reconstruction of a signal with discrete sampled data, the sampling rate must comply with the Nyquist theorem, which assumes sampling at uniform time steps. Nyquist frequency is defined as the minimum required sampling frequency for a given signal bandwidth which permits reconstruction of the signal without loss of information. If one assumes that an appropriate band-limiting filter precedes the analog-to-digital converter, then aliasing is minimized. In practice, the sampling frequency employed in actual implementations is characteristically greater than the (sometimes twice, depending on the definition) Nyquist frequency to reduce distortion of the digital instantiation of the signal.
The Problem of detecting an unknown signal somewhere in a large spectral region is typically dealt with via one of the following approaches: (A) Full (Nyquist) rate sampling of the large spectral region with a high sample rate analog-to-digital converter to recover the signal; B) Analog (pre-filter) sub-banding followed by (Nyquist) sampling of analog sub-bands and sub-band channel equalization; or C) Random demodulation combined with compressive sensing.
Method A is a frequently employed technique which utilizes very high speed analog-to-digital convertor (ADC) technology. However, high speed analog-to-digital conversion may be limited by dynamic range restrictions. Method B is commonly invoked to overcome analog-to-digital converter dynamic range limitations. This approach employs a massively parallel implementation wherein the wide frequency region of interest is partitioned into sub-bands by parallel analog band-pass filters. Method B requires equalization among adjacent analog sub-band partitions. Method C is a classical single channel random demodulator (discussed in literature) followed by compressive sensing to unwrap the aliased narrow-band spectrum resulting from under sampling. This approach works well for detection of sparse (narrow-band) signals across the wide band of interest. Method C is not suitable for recovery of wideband signals.
FIG. 1 shows a (Method A) conventional channelized receiver. In this approach, a wide band input analog signal X(t), with a frequency of 4 GHz (example), is input to an anti-aliasing filter 102 to reject signals outside of the band of interest. The anti-aliasing BPF (102) filter attenuates signals outside of the spectrum of interest. A full Nyquist rate analog-to-digital converter (ADC) 104 with a sampling frequency Fs, equal to or greater than the Nyquist frequency of the input signal, samples the output of the anti-aliasing filter, converting the analog signal to a digital signal. The output of the ADC 104 is then channelized by a (fixed resolution) filter bank 106. The full Nyquist rate ADC (104) samples the entire signal spectrum of interest. Sampled data are separated via a uniform fixed filter bandwidth (106). The channelizer (filter bank) 106 decomposes the wideband signal into equally spaced partitions. Estimated X(t) suffers from ADC dynamic range (maximum to minimum signal) limitation; and distortion (ripple & group delay) of signals wider than the channelizer fixed filter bandwidth.
Method B is frequently employed to bypass ADC sample rate and spur free dynamic range constraints by employing lower speed, higher dynamic range ADCs. In this approach, reconstruction of the original signal set with minimum distortion requires adaptive equalization to minimize phase & magnitude distortion among adjacent filter cross over regions, and filter pass band ripple distortion. An artifact that is difficult to overcome in this method is rejection of adjacent pass-band filter stop band leakage resulting from finite (analog) filter stop band rejection.